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lfunc_lfunctions • Show schema
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{'Lhash': '1477599240692567740766805708580', 'a10': [1.3691023861848555, 0.0], 'a2': [0.0, 2.1700864866260337], 'a3': [1.0, 0.0], 'a4': [-2.7092753594369228, 0.0], 'a5': [0.0, -0.6308976138151446], 'a6': [0.0, 2.1700864866260337], 'a7': [0.0, 1.0], 'a8': [0.0, -1.5391888728108891], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [0, -1.0]]], [13, [[1.0, 0], [2.1700864866260337, -2.8793618460629564]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.64', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '3049001357904625564797417190756', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.1700864866260337], [-2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0.6308976138151446], [-5.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -5.709275359436923], [-11.0, 0]], [[1.0, 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'3.00785803725823986099478664974931', '3.41077632709286330860510459862566', '4.98543438906148982988847618256669', '6.56506880454803847528069253209026', '8.034362462366570949678226393235525', '8.811975164797798970238473440675438', '10.08657142583933243525912579528978', '10.50058292325122204817204286754357', '11.43432955357083461865826726519942'], 'prelabel': '2-273-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.7944210571409469, 'root_number': '-0.7985912905072801 - 0.6018736999785894*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.39721052857', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16562027456661869061557140713', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.00785803725823986099478664975', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41077632709286330860510459863', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '13.12', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/c/b/64/6'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-273-13.12-c1-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-273-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.39721052857047345, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16562027456661869061557140713', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1477599240692567740766805708580', 'Lhash_array': ['1477599240692567740766805708580'], 'label': '2-273-13.12-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/c/b/64/6'}